Suppose that the curve C in Figure 7 has the polar equat
Question and Solution
Suppose that the curve C in Figure 7 has the polar equation r = f (? ). (a) Show that c(? ) = (f (? ) cos ? , f (? )sin
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Suppose that the curve C in Figure 7 has the polar equation r = f (? ). (a) Show that c(? ) = (f (? ) cos ? , f (? )sin ? ) is a counterclockwise parametrization of C. (b) In Section 11.4, we showed that the area of the region R is given by the formula Area of R = 1 2 ? ? f (? )2 d? Use the result of Exercise 37 to give a new proof of this formula. Hint: Evaluate the line integral in Eq. (1) using c(? ).
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